B Y Menfuration of fuperficies is underflood, how to take the neceffary dimenfions of any plain, and by these dimenfions to plan, or reprefent in plano any furface proposed, and alfo to comptute the areas or contents in fome known measures as inches, feet, yards, roods, perches, acies, miles, &c. As may be moft convenient for the purples of the feveral artificers, whofe works are measured, as plain figures. Or preparatory to the meafuring of flids gauging, or finding the capacities of vessels; also in furveying, &c. The dimenfions of the ends of folids, and bottoms or tops of veffels, are moftly taken in inches, and their areas computed in inches and decimal parts. The contents of board, plank, and windows, are moftly expreffed in feet. Joiners work, Mafons work, Plaiftering, Painting, Paving, Roofing, &c. are measured by the yard. Land is measured by the perch according to ftatute 16 feet and a half to the perch, and its content is expreffed in acres, roods, and perches, the areas of kingdoms, empires and of the zones are computed in fquare miles. Problem ift. To Measure a Square. Fig. 11. Definition. A fquare is a plain having 4 equal fides, and 4 equal right angles. Dimenfions. Measure one fide. RUE E. Multiply the fide into its felf, and the product is the the area, of the fame name as the dimenfion. If the diagonal of a fquare be given, to find the area. half the fquare thereof is the area, or half the diagonal fquared and doubled is the content. If the fide of a fquare be 125 inches, query its area? Definition. A parallelogram has 2 equal fides, 2 equal ends, and 4 equal right angles, confequently the fides and ends are parallel. Dimenfions Dimenfions. Measure one fide, and one end. RULE. The product of the fide and end, or the product of the length and breadth is its area, or content. But if the length be in feet, and the breadth in inches as in board meafure, then 1 twelfth of the product of the length and breadth, is the content in feet. If the length of a parallelogram be 64 inches, and the breadth 30 inches, required its area? Problem 3d. To Measure a Rhombus. Fig. 13 Definition. A rhombus is a plain figure, under 4 equal fides, having two equal acute angles, and two equal obtufe angles. Dimenfions. Measure one fide, and a perpendicular from one obtufe angle to the oppofite fide. RULE. Multiply the faid fide by the perpendicular, and the product is the area. is N. B. A regular rhombus, is when the acute 60 degrees, and the perpendicular falls on the middle of the oppofite fide; then having the fide given. If from the fquare of the fide you fubtract a fourth part of that fquare, the fquare root of the remainder is equal to the perpendicular. But if the acute be lefs or more than 60 degrees, and the fide and acute angle given, the perpendicular is found thus, as radius: fide :: fine of acute angle the perpendicular. If If the fide of a regular rhombus be 50 inches, required its area? 50×50—50×50 43.3 the perpendicular, and 4 43.3 × 50 1082.5 inches, anfwer. Problem 4th. To Measure a Rhomboides. Fig. 14. Definition. This figure has fuch a relation to a rhombus, as a parallelogram has to a square, having two equal parallel fides, and two equal parallel ends, and angles as a rhombus. Dimenfions. Length and perpendicular breadth, to be measured. RULE. The product of the two dimenfions is the area. If the fide, and end, with the acute angle be given, you may fay as radius end: fine of that angle: its perpendicular breadth. If the length of a rhomboides be 90 and its perpendicular breadth 25 inches, query its area or content ? zd. If the length be 90, end 36 inches, and the acute angle 38 degrees 20 minutes required its area? Then as radius god. oom.: 36 :: fine of angle 38d. 20m. 22.32 or As 36 .62 the natural fine of 38d. 20m. : 22.32 the perpendicular. 22.32 X 90 = 2008.8 the area. Problem Problem 5th. To Measure a Triangle. Fig. 15. Definition. Every triangle, has three fides, and three angles. Dimenfions. Measure the bafe and perpendicular. RULE. Multiply the bafe by one half the perpendicular, and the product is the area; for every triangle is one half its circumfcribing parallelogram. N. B. An equilateral triangle has three equal fides and three equal angles. A right angled triangle has one right angle. A fcalene triangle has three unequal fides and no right angle. If the three fides of a triangle be given, to find its area without a perpendicular, RULE. From half the fum of the three fides fubtract each fide, then multiply that half fum by one remainder, and that product by another remainder, and the new product by the third remainder, then the fquare root of the laft product is the area of the triangle. If the bafe of a triangle be 126, and the perpendi cular be 80, query its area? 80 126 X 2 5040 the area or content. Problem 6th. To Measure a Trapezia. Fig. 16. Definition. This figure has 4 unequal fides, and 4 unequal angles. Dimenfions. Measure a diagonal and all the fides. Then you may plan it, and meature the perpendiculars from your plan. Or meafure the diagonal, and the perpendiculars |